Undeterred by charges that the GOP is too focused on social issues, Senate Republicans are gunning for a fight this fall over the hot-button subject of late-term abortions.

Flanked by anti-abortion groups, Sen. Lindsey Graham (R-S.C.) will unveil legislation on Thursday to federally ban abortions after five months of pregnancy.

Graham’s move comes at a crucial juncture for the GOP, often mired in disagreements over political strategy on matters that affect women, minorities and gays. The Senate, for example, is poised Thursday to pass legislation that would ban workplace discrimination against LGBT employees — a bill expected to draw a handful of Republican supporters.

A recent Quinnipiac poll found 55 percent of voters support the 20-week limit, one of a slew of polls that have Republicans betting that late-term abortion will unite the GOP in ways other issues don’t.

Graham and co-sponsors like Sens. Roy Blunt (R-Mo.) and Chuck Grassley (R-Iowa) see an issue in which the party is on the right side of public sentiment. And if Graham’s bill is successful, it could lead to further gains on restricting abortion, they say.

“You gotta work pretty hard to find anything but a huge majority” in support of the legislation, Blunt said. “We continue to see public opinion toward protecting life. But you’re not going to win the debates if you start at a place where you don’t have a majority believing that’s the right thing to do.”

There’s an added benefit in that the measure could help shore up the right flank for Graham, who is often viewed with deep suspicion by tea party-aligned conservatives particularly after he supported the Senate’s immigration bill. Anti-abortion groups said the legislation is sure to help Graham fight challengers on the right next year.

“There is a political advantage to anyone who is the lead sponsor,” said David Christensen, a lobbyist at the Family Research Council.

That lead sponsor was supposed to be Sen. Marco Rubio (R-Fla.), who also raised eyebrows on the right for his leadership on the Senate immigration bill. Rubio backed off amid questions surrounding the drafting of the bill.

Groups pushing abortion restrictions don’t seem to care whether Graham is being motivated by politics — as long as he helps push the bill across the finish line.

“If Lindsey is backing this legislation because it will help him politically, I don’t see how that’s bad for us,” said Ralph Reed, chairman of the Faith & Freedom Coalition.

“It’s a dangerous game discerning people’s motives. If this does end up helping him then he deserves the credit,” said Susan B. Anthony List President Marjorie Dannenfelser. “Frankly, he’s the ideal guy to do this.”

Graham said in an interview that the legislation is less about politics, more about conscience.

“The government has a legitimate interest in protecting the unborn child over the 20-week period because they are capable of feeling pain and the scientific evidence is overwhelming,” Graham said. “When you do surgery on a 20-week baby, you provide anesthesia because of pain.”

Democrats are more than willing to have the debate, seeing the issue as an electoral loser for Republicans.

In July, Senate Majority Leader Harry Reid (D-Nev.) said he’s “open” to allowing a vote on the bill, though a leadership aide doubted that a vote would occur soon. Sen. Patty Murray of Washington, the former head of the Senate Democrats’ campaign arm, said Republicans will embrace Graham’s bill “at their own peril.”

Murray pointed to Ken Cuccinelli’s loss in the Virginia gubernatorial race this week along with that of a tea party House candidate in Alabama as further repudiations of the GOP’s social agenda.

“The American people have spoken loudly, that they want us to focus on jobs and the economy, and they don’t want Congress to keep treading on their rights to access to health care,” Murray said. “In election after election, people have said: ‘Focus on jobs, not on attacking women’s health.’”

The bill’s introduction — and its subsequent media coverage — will serve to boost enthusiasm for Republicans among their conservative base as electoral politics creep into every decision on Capitol Hill as the midterms loom a year away. But Graham’s fellow senators and outside allies also know the bill allows them to get out front of Democrats on social issues, which many believe contributed to Cuccinelli’s loss.

“It’s a much better thing to be campaigning on than rape and incest these days,” Dannenfelser said, referring to intemperate remarks on those subjects by failed conservative Senate candidates last year.

Reed of the Faith & Freedom Coalition said Graham’s bill will be a key messaging device for the party’s attempt to take back the Senate next year. It will allow Republicans to talk about abortion legislation in a form that polls show most Americans support — and serve as a prebuttal for Democrats hungry for GOP candidate missteps.

“If you’re the Republican Party, praying that these issues won’t come up is a losing strategy. They’re going to come up,” Reed said. “I would urge Republicans … to get their head out of the sand and realize that social and cultural issues are going to come up.”

Even though aides from both parties largely see Graham’s bill as a messaging device, pro-choice groups still see it as a threat, both because of Graham’s status as a skilled Senate legislator and because he’s a consistent supporter of anti-abortion legislation. As a House member, he led a successful effort that legally recognized in utero children killed during crimes as victims.

If Graham’s bill did come up for a vote, there are plenty of centrist lawmakers — many of them Democrats — who anti-abortion and pro-choice groups would both lobby to see their sides of the issue, said Donna Crane, NARAL Pro-Choice America’s policy director.

“We don’t have a pro-choice majority in the Senate. So we’re both going to be fighting for senators,” she said.

A bill otherwise identical to Graham’s bill passed the House earlier this year, pointing to both the Commerce Clause and the 14th Amendment as justification for congressional authority to pass a federal 20-week abortion ban. Graham’s bill will include no such constitutional enumeration.

“I’m just going to remain silent on that. We’re not a court, we’re a legislative body,” Graham said.

After appearing eager to lead the bill, Rubio held off until conservatives could sort out the constitutional language. Rubio said on Tuesday that he supports Graham’s leadership and the underlying legislation, but remains worried about the bill being held up in the courts if it were to become law.

“I’m not looking for a symbolic measure, so we certainly want something that can withstand judicial scrutiny,” Rubio said.

Late Wednesday, the Florida senator decided he will be a co-sponsor, an aide said. Anti-abortion sources believe other conservatives like Sens. Mike Lee of Utah, Ted Cruz of Texas and Rand Paul of Kentucky won’t be far behind.